Finite Group Databasebeta

← #20242065

Subgroups — #20242065

Order 6016.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689147C211yesmaximal, characteristic, complemented
2C2×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#15688869C212yesmaximal, complemented
4#15688867C212yesmaximal, complemented
5C47×#532C211yesmaximal, characteristic
6C2×#10625329—21no—
7C22×C47⋊C8—21no—
8C4⋊(C47⋊C8)—21no—
9C4⋊(C47⋊C8)—21no—
10C4⋊(C47⋊C8)C2212yes—
11C4⋊(C47⋊C8)C2212yes—
12C2×#41×C47—21no—
13C4⋊Q8×C47C2211yescharacteristic
14#127×C47C2211yescharacteristic
15#124×C47—21no—
16#121×C47—21no—
17#121×C47C412yes—
18C4×D4×C47—21no—
19C4×D4×C47C412yes—
20C2×C42×C47C2211yescharacteristic
21#41×C47—42no—
22#41×C47—42no—
23C2×Q8×C47—21no—
24C2×D4×C47—22no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47C2×C412yes—
28C22×C4×C47—22no—
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C4⋊C4×C47—21no—
33C4⋊C4×C47C2×C412yes—
34C22⋊C4×C47—22no—
35C22⋊C4×C47—22no—
36C42×C47C2×C411yescharacteristic
37C42×C47D411yescharacteristic
38C42×C47D411yescharacteristic
39C42×C47C2311yescharacteristic
40#10625329—42no—
41C2×C47⋊C8—22no—
42C2×C47⋊C8—22no—
43C2×C47⋊C8—42no—
44C23×C47—22no—
45C23×C47C22⋊C411yescharacteristic
46Q8×C47—41no—
47Q8×C47—41no—
48D4×C47—42no—
49D4×C47—44no—
50D4×C47—41no—
51D4×C47—41no—
52D4×C47—41no—
53D4×C47—41no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—22no—
57C2×C4×C47—41no—
58C2×C4×C47—44no—
59C2×C4×C47C22⋊C411yescharacteristic
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47D812yes—
63C2×C4×C47SD1612yes—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C47⋊C8—42no—
68C47⋊C8—42no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47—42no—
72C22×C47—42no—
73C22×C47—42no—
74C22×C47#10212yes—
75C22×C47C2×C22⋊C411yescharacteristic
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—42no—
80C4×C47#10212yes—
81C4×C47C2×D811yescharacteristic
82C4×C47C2×SD1611yescharacteristic
83C4×C47AGL(1,ℤ/8)11yescharacteristic
84C4×C47#13711yescharacteristic
85#1547—471nomaximal, Sylow
86C2×C47—22no—
87C2×C47—82no—
88C2×C47#41311yescharacteristic
89C2×C47C2×#10211yescharacteristic
90C2×C47#41711yescharacteristic
91#532D4711yescharacteristic
92#423—471no—
93C2×C4⋊C8—471no—
94#332—472no—
95#331—472no—
96C47#154711yescharacteristic, complemented, Sylow
97C2×#41—21no—
98C2×M16—941no—
99C22×C8—941no—
100C4⋊Q8C2×D4711yescharacteristic
101#127C2×D4711yescharacteristic
102#124—21no—
103#121—21no—
104#121Dic4712yes—
105C4×D4—21no—
106C4×D4Dic4712yes—
107C2×C42C2×D4711yescharacteristic
108C4⋊C8—472no—
109C4⋊C8—472no—
110C4⋊C8—941no—
111C4⋊C8—941no—
112#41—42no—
113#41—42no—
114C2×Q8—21no—
115C2×D4—22no—
116C2×D4—21no—
117C2×D4—21no—
118C2×D4C2×Dic4712yes—
119C22×C4—22no—
120C22×C4C2×Dic4711yescharacteristic
121C22×C4C22⋊D4711yescharacteristic
122C22×C4C22⋊D4711yescharacteristic
123M16—1882no—
124C2×C8—942no—
125C2×C8—942no—
126C2×C8—1882no—
127C4⋊C4—21no—
128C4⋊C4C2×Dic4712yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C42C2×Dic4711yescharacteristic
132C42C22⋊D4711yescharacteristic
133C42C22⋊D4711yescharacteristic
134C42C22×D4711yescharacteristic
135C23—22no—
136C23C22⋊Dic4711yescharacteristic
137Q8—41no—
138Q8—41no—
139D4—42no—
140D4—44no—
141D4—41no—
142D4—41no—
143D4—41no—
144D4—41no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—44no—
150C2×C4#1062533412yes—
151C2×C4#1062533512yes—
152C2×C4C22⋊Dic4711yescharacteristic
153C2×C4C22⋊Dic4711yescharacteristic
154C2×C4C22⋊Dic4711yescharacteristic
155C2×C4C22×Dic4711yescharacteristic
156C2×C4C2×C22⋊D4711yescharacteristic
157C2×C4C2×C22⋊D4711yescharacteristic
158C8—1882no—
159C8—1882no—
160C22—21no—
161C22—21no—
162C22—42no—
163C22—42no—
164C22—42no—
165C22#1309394512yes—
166C22C2×C22⋊Dic4711yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—42no—
171C4#1309394512yes—
172C4C2×#1062533411yescharacteristic
173C4C2×#1062533511yescharacteristic
174C4#1309404911yescharacteristic
175C4#1309405411yescharacteristic
176C2—22no—
177C2—82no—
178C2#1568910711yescharacteristic
179C2C2×#1309394511yescharacteristic
180C2#1568912411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#532C2
socleC22×C47C2×C22⋊C4
hypercenter#532D47
hypocenterC47#1547
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689147C2semidirect
2. C2×C4⋊(C47⋊C8)C2semidirect
3. #15688869C2semidirect
4. #15688867C2semidirect
96. C47#1547semidirect